{
  "id": 3570,
  "curve_key": "3013216051307536:-164921949667784515534784",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-62775334402240",
    "190881907114676878912"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 106.92535307658888,
  "faltings_height": 6.724492818081768,
  "conductor": "10674865284720",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "37",
    "41",
    "43",
    "59",
    "127"
  ],
  "discriminant": "92105432614722265086892390233170434560000",
  "regulator": "2438.884293128970803398924407952527388297491092",
  "points": [
    [
      "62848297/16",
      "141755403699/64"
    ],
    [
      "100702834/121",
      "15704293591350/1331"
    ],
    [
      "691169826/169",
      "3509493787450/2197"
    ],
    [
      "2158912576/529",
      "19849276235880/12167"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "Inspired by (much better) curve#3566\r\nSpecialized curve of the C2 x C4 family y^2 = x(x+u^2)(x+v^2), where u±v=d*w^2. Here (u,v)=(1270,7462), with v-u=6192=43*12^2. PARI/GP gives exact rank 4 and torsion C2 x C4.",
  "created_at": "2026-09-28 19:19:22",
  "updated_at": "2026-09-28 19:19:22"
}